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Dynamical Behaviors of a Discrete SIR Epidemic Model with Nonmonotone Incidence Rate

Trija Fayeldi, Agus Suryanto, Agus Widodo


In this paper, Euler method is applied to discretize a SIR epidemic model with nonmonotone incidence rate. The obtained discrete dynamical system is then analyzed, specifically we determine the existence and stability of fixed points. It is shown analytically and numerically that the discrete model is dynamically consistent with its continuous model only for relatively small step-size. Moreover, numerical simulations not only illustrate the results, but also show the rich dynamics behaviors of the discrete system such as periodic solution and bifurcation.


discrete model, nonmonotone incidence rate, Euler method, fixed points, stability, bifurcations.

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